Homework Assignments for Linear Algebra: Johnson, Reiss, Arnold

These assignments are still being adjusted, but you should assume that these are correct until told otherwise.

Chapter 1

 

 

Linear Systems,
Augmented Matrices, Elementary Row Operations

1.1

1-6, 12-14, 16-18, 20, 22, 27-28, 34, 35

Echelon Form, Reduced E-F,
Gauss-Jordan Elimination

1.2

2-18 x2; 24, 31-33, 38, 39, 41, 42, 44, 47, 50, 52, 54

Consistent systems, Homogeneous systems, Multiple solutions,  Applications

1.3

1, 4, 8-18x2; 19-21, 24, 26-30x2

Networks, Circuits

1.4

1, 3, 5, 6, 8

Matrix Algebra

1.5

3-48x3; 61, 65, 69

Symmetry, transpose, etc

1.6

3-24x3; 32;
(Equation 3 is the list of matrices at the beginning of the exercise set.)  36, 41. 
Read, and prepare for class: 47, 48, 49.

Linear Independence, Dependence,
Nonsingular matrices

1.7

3-42x3; 53

Inverses

1.9

3-21x3; 24, 25, 27, 28, 30, 32, 36, 38, 60, 66.

Chapter 2

 

 

Plane Vector Geometry

2.1

1, 2, 5, (Do, but do not hand in: 15, 17.)  21, 25, 26, 29, 31, 32, 35.

Vectors in 3-D

2.2

3-33x3.

Dot product, Cross product

2.3

3-48x3.

Lines and Planes in Space

2.4

1-25 odd

R3

3.1

1, 2, 5, 9, 10, 11, 13, 16, 19, 21, 22, 27

Rn as a Vector-Space

3.2

1-15 0dd , 21, 22, 23

Subspace examples

3.3

1-11 odd, 12-18 even.

Bases

3.4

3-27x3

Dimension

3.5

3-36x3

Orthogonal bases

3.6

2-10 even, 13-19 odd.

Linear Transformations

3.7

1, 3, 18, 19, 22

Eigenvalues for 2x2 matrices

4.1

1-7, 9, 11

Determinants

4.2

2-18 even

Determinants and row operations

4.3

1-11 odd, 23

Characteristic polynomial

4.4

3-18x3

Eigenspaces

4.5

1-11.